Nonlinear phenomena are often encountered in various practical systems, and most of the nonlinear problems in science and engineering can be simply described by nonlinear equation, effectively solving nonlinear equation (NE) has aroused great interests of the academic and industrial communities. In this paper, a robust zeroing neural network (RZNN) activated by a new power versatile activation function (PVAF) is proposed and analyzed for finding the solutions of dynamic nonlinear equations (DNE) within fixed time in noise polluted environment. As compared with the previous ZNN model activated by other commonly used activation functions (AF), the main improvement of the presented RZNN model is the fixed-time convergence even in the presence of noises. In addition, the convergence time of the proposed RZNN model is irrelevant to its initial states, and it can be computed directly. Both the rigorous mathematical analysis and numerical simulation results are provided for the verification of the effectiveness and robustness of the proposed RZNN model. Moreover, a successful robotic manipulator path tracking example in noise polluted environment further demonstrates the practical application prospects of the proposed RZNN models.

非线性现象在各种实际系统中经常遇到，科学和工程中的大多数非线性问题都可以用非线性方程简单地描述，有效地解决非线性方程（NE）引起了学术界和工业界的极大兴趣。本文提出了一种新的幂次通用激活函数（PVAF）激活的鲁棒归零神经网络（RZNN），并对其进行了分析，以寻找在噪声污染环境中固定时间内的动态非线性方程（DNE）的解。与之前由其他常用激活函数（AF）激活的ZNN模型相比，所提出的RZNN模型的主要改进是即使在存在噪声的情况下，固定时间收敛。此外，所提出的RZNN模型的收敛时间与其初始状态无关，它可以直接计算。提供了严格的数学分析和数值模拟结果，以验证所提出的RZNN模型的有效性和鲁棒性。此外，在噪声污染环境中成功的机器人机械手路径跟踪示例进一步证明了所提出的RZNN模型的实际应用前景。